A Plan Goal Graph (PGG) represents plan-goal relationships in a hierarchical structure. Plans and goals are decomposed following their means-ends relationships. A goal node in the PGG has plan nodes as children, which explicitly represent the alternative plans to achieve the goal. A plan node in the PGG has goal nodes as children, each of which represents a sub-goal of the planned task, collectively defines the objective of the plan. The leaf nodes are plan nodes corresponding to primitive actions that can be carried out in unit steps (e.g., carrying out a sequence of steps to execute a pre-defined operation).
Bayesian network (BN) (also called belief networks, or causal networks) is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). A BN is a DAG where nodes represent random variables and edges represent conditional dependencies. Each node has an associated conditional probability table (CPT) that quantifies the conditional probability distribution over the states of the node given different combinations of the states of the parent nodes.
Bayesian network has been increasingly used for representing probabilistic knowledge. BN compactly represents the probabilistic dependencies among domain variables with the graphical structure. This quantified dependence representation provides a powerful reasoning platform following the Bayes' Theorem. Efficient algorithms have been developed to perform inference even with partial observation of variable states. In a Bayesian network, the posterior probabilities of variables can be computed given any other variables' state observations. The numerical value of posterior probabilities provides a quantitative estimation of the possible states of the unobserved variables. In the mission planning scenario, if the mission plans and goals are represented in Bayesian network models, the reasoning power of Bayesian networks can be used to evaluate the plans' feasibility and the goals' achievability.
Both PGG and BN are acyclic directed graph where nodes represent domain variables and arcs represent dependence relationships between the nodes. In PGG, a node is either a plan node or a goal node. Arcs from a plan node to its sub-goal nodes indicates collective relationship among all these sibling sub-goal nodes, i.e., all sub-goals must be met to complete the plan. Arcs from a goal node to its sub-plan nodes indicates alternative relationships among all these sibling sub-plan nodes, i.e., the goal may be met by choosing any of the plans.
By separating goals, plans, and sub-plans (i.e. actions to be performed to achieve the goals), a PGG is relatively easy for a person to create and understand. While PGG is an intuitive mission representation, it is informal and provides no formal reasoning theoretical foundation and practical mechanisms to compute probabilistic outcomes and based on which to reason and determine the course of actions. BN, on the other hand, is a formal probabilistic reasoning model with a rigorous theoretical foundation. Constructing a mission model in BN directly is challenging for complex mission systems (e.g., mission execution by autonomous vehicles) because of its lack of intuitive notation of plan-goal hierarchical decomposition.
Thus, a heretofore unaddressed need exists in the industry to address the aforementioned deficiencies and inadequacies.